A five-finger exercise is a musical composition designed primarily to exercise all five fingers of the hand. A typical example is Hanon's The Virtuoso Pianist in 60 Exercises.
Chopin wrote a number of études (studies) that are widely regarded as musical compositions to train musical ability and dexterity of the fingers, especially Étude opus 10. Another example of an exercise to develop musical skills may be Für Elise, it has been suggested that it was written as an exercise to practice skills on the piano. It has since been rewritten for many other instruments.
The technique has also been part of scientific study. Another example being The art of piano playing: a scientific approach by George A. Kochevitsky, who explains some of the fundamentals in teaching the piano. In his chapter on Progressive ideas in nineteenth-century teaching he explains some of Chopin's idea's (see above), there is a mention of five-finger exercises.
By analogy, the term is also used to describe exercises solely for the development of a skill: for example, asking students to solve questions in philosophy or economics. It is also described as a method for becoming "Good Christians" by Walter Scott. Another analogy is described on the Western Washington University website as part of The Relaxation & Stress Reduction Workbook.